Technical Abstract:
Geometric properties of elementary particles, aggregates, peds, pores, exposed soil surfaces, contours, etc., are of utmost importance for understanding and managing soils. Ideal geometrical objects are widely used in measurements in soil science, and this introduces uncontrollable errors. Fractal geometry was developed to describe irregular natural shapes having hierarchies of ever-finer detail and to relate features of natural objects observed at different scales. The application of fractal models in soil science is a burgeoning field. We present a compendium of methods to perform fractal analysis of soils and show both the challenges and opportunities of using fractals in soil studies. Physical models of emerging fractal scaling are discussed that are relevant to soil structure and functioning. Indirect measurements are listed that can be a source of data in application of fractal models. Sources and the magnitude of uncertainty in fractal parameters of soils are discussed with the stipulation of relationships of fractal geometry being only approximately true in soils. Multiple uses of fractal parameters are described, including structure parameterization and simulation, explanation of iterative processes of soil formation, defining transition scales and representative elementary volumes, uncovering the underlying chaos in soils, local approximation of soil variability in remote sensing, parameterization and simulation of water floe and contaminant transport in soils, quantifying pedodiversity to design ecological preserves, and compression of soil heterogeneity data.